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Birkhäuser

Topological Nonlinear Analysis

Degree, Singularity, and Variations

  • Book
  • © 1995

Overview

Editors:
  1. Michele Matzeu

    1. Department of Mathematics, University of Rome, Tor Vergata, Rome, Italy

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    You can also search for this editor in PubMed   Google Scholar

  2. Alfonso Vignoli

    1. Department of Mathematics, University of Rome, Tor Vergata, Rome, Italy

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 15)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
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  2. Variational Methods and Nonlinear Problems: Classical Results and Recent Advances

    • Antonio Ambrosetti
    Pages 1-36

  3. Introduction to Morse Theory a New Approach

    • Vieri Benci
    Pages 37-177

  4. Applications of Singularity Theory to the Solutions of Nonlinear Equations

    • James Damon
    Pages 178-302

  5. Positivity of Maps and Applications

    • E. N. Dancer
    Pages 303-340

  6. Topological Bifurcation

    • Jorge Ize
    Pages 341-463

  7. Critical Point Theory and Applications to Differential Equations: A Survey

    • Paul H. Rabinowitz
    Pages 464-513

  8. Symplectic Topology: An Introduction

    • Claude Viterbo
    Pages 514-531

  9. Back Matter

    Pages 533-534
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Keywords

About this book

Topological tools in Nonlinear Analysis had a tremendous develop­ ment during the last few decades. The three main streams of research in this field, Topological Degree, Singularity Theory and Variational Meth­ ods, have lately become impetuous rivers of scientific investigation. The process is still going on and the achievements in this area are spectacular. A most promising and rapidly developing field of research is the study of the role that symmetries play in nonlinear problems. Symmetries appear in a quite natural way in many problems in physics and in differential or symplectic geometry, such as closed orbits for autonomous Hamiltonian systems, configurations of symmetric elastic plates under pressure, Hopf Bifurcation, Taylor vortices, convective motions of fluids, oscillations of chemical reactions, etc . . . Some of these problems have been tackled recently by different techniques using equivariant versions of Degree, Singularity and Variations. The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in Nonlinear Analysis during the last two-three decades. The survey articles presented here reflect the personal taste and points of view of the authors (all of them well-known and distinguished specialists in their own fields) on the subject matter. A common feature of these papers is that of start­ ing with an historical introductory background of the different disciplines under consideration and climbing up to the heights of the most recent re­ sults.

Editors and Affiliations

  • Department of Mathematics, University of Rome, Tor Vergata, Rome, Italy

    Michele Matzeu, Alfonso Vignoli

Bibliographic Information

  • Book Title: Topological Nonlinear Analysis

  • Book Subtitle: Degree, Singularity, and Variations

  • Editors: Michele Matzeu, Alfonso Vignoli

  • Series Title: Progress in Nonlinear Differential Equations and Their Applications

  • DOI: https://doi.org/10.1007/978-1-4612-2570-6

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1995

  • Hardcover ISBN: 978-0-8176-3742-2Due: 22 December 1994

  • Softcover ISBN: 978-1-4612-7584-8Published: 22 September 2011

  • eBook ISBN: 978-1-4612-2570-6Published: 06 December 2012

  • Series ISSN: 1421-1750

  • Series E-ISSN: 2374-0280

  • Edition Number: 1

  • Number of Pages: 531

  • Topics: Analysis, Topology

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